A unified analytical parametric method for kinematic analysis of planar mechanisms

Abstract

This paper describes a method for unified parametric kinematic analysis of those planar mechanisms whose geometry can be defined with a set of independent vectorial loops, i.e. solvable independently; this covers a wide range of planar mechanisms. The method is developed by employing the well-known vectorial illustration, and vectorial-loop equations solved with the aid of complex polar algebra leading to a total of only nine unified/generic one-unknown parametric equations consisting of five equations for position analysis and two equations for velocity and acceleration analysis each. Then, the kinematics of joints and mass centers are manifested as resultants of a few known vectors. This method is needless of relative-velocities, relative-accelerations, instantaneous centers of rotation and Kennedy’s Theorem dominantly used in the literature, especially textbooks. The efficiency of the method is demonstrated by its application to a complex mechanism through only eight unified equations, and simultaneously compared to the solution using the textbook common (Raven’s) method which required the derivation of 67 extra equations to get the same results. This reveals the fact that the method is not only a powerful tool for mechanical designers but a most powerful and efficient method for teaching and learning the kinematics of planar mechanisms.